
"""simple docstring"""



from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray


def lowerCamelCase_				(     _lowerCamelCase			:	str					,				_lowerCamelCase			:	Union[str, Any]					,				_lowerCamelCase			:	Union[str, Any]					,				_lowerCamelCase			:	Union[str, Any]					,				):
       lowerCamelCase_							,							lowerCamelCase_       							=		coefficient_matrix.shape
       lowerCamelCase_							,							lowerCamelCase_       							=		constant_matrix.shape

       if rowsa != colsa:
              lowerCamelCase_       							=		F"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
              raise ValueError(snake_case__				)

       if colsa != 1:
              lowerCamelCase_       							=		F"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
              raise ValueError(snake_case__				)

       if rowsa != rowsa:
              lowerCamelCase_       							=		(
                  '''Coefficient and constant matrices dimensions must be nxn and nx1 but '''
                  F"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
              )
              raise ValueError(snake_case__				)

       if len(snake_case__				) != rowsa:
              lowerCamelCase_       							=		(
                  '''Number of initial values must be equal to number of rows in coefficient '''
                  F"""matrix but received {len(snake_case__				)} and {rowsa}"""
              )
              raise ValueError(snake_case__				)

       if iterations <= 0:
              raise ValueError('''Iterations must be at least 1'''				)

       lowerCamelCase_       							=		np.concatenate(
           (coefficient_matrix, constant_matrix)					,				axis=1				)

       lowerCamelCase_							,							lowerCamelCase_       							=		table.shape

       strictly_diagonally_dominant(snake_case__				)

       # Iterates the whole matrix for given number of times
       for _ in range(snake_case__				):
              lowerCamelCase_       							=		[]
              for row in range(snake_case__				):
                     lowerCamelCase_       							=		0
                     for col in range(snake_case__				):
                            if col == row:
                                   lowerCamelCase_       							=		table[row][col]
                            elif col == cols - 1:
                                   lowerCamelCase_       							=		table[row][col]
                            else:
                                   temp += (-1) * table[row][col] * init_val[col]
                     lowerCamelCase_       							=		(temp + val) / denom
                     new_val.append(snake_case__				)
              lowerCamelCase_       							=		new_val

       return [float(snake_case__				) for i in new_val]


def lowerCamelCase_				(     _lowerCamelCase			:	int				):
       lowerCamelCase_							,							lowerCamelCase_       							=		table.shape

       lowerCamelCase_       							=		True

       for i in range(0					,				snake_case__				):
              lowerCamelCase_       							=		0
              for j in range(0					,				cols - 1				):
                     if i == j:
                            continue
                     else:
                            total += table[i][j]

              if table[i][i] <= total:
                     raise ValueError('''Coefficient matrix is not strictly diagonally dominant'''				)

       return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
 import doctest

 doctest.testmod()





"""simple docstring"""




def        a__					(							snake_case__							)		->   list:

			if len(snake_case__							) <= 1:
						return [tuple(snake_case__							)]

			lowerCamelCase      =   []

			def generate(snake_case__			,					snake_case__							):
						lowerCamelCase      =   [0] * n
						res.append(tuple(snake_case__							)							)

						lowerCamelCase      =   0
						while i < n:
									if c[i] < i:
												if i % 2 == 0:
															lowerCamelCase ,  lowerCamelCase      =   arr[i], arr[0]
												else:
															lowerCamelCase ,  lowerCamelCase      =   arr[i], arr[c[i]]
												res.append(tuple(snake_case__							)							)
												c[i] += 1
												lowerCamelCase      =   0
									else:
												lowerCamelCase      =   0
												i += 1

			generate(len(snake_case__							)			,					snake_case__							)
			return res


if __name__ == "__main__":
					lowerCAmelCase				:     str					=				input("""Enter numbers separated by a comma:\n""").strip()
					lowerCAmelCase				:     List[Any]					=				[int(item) for item in user_input.split(""",""")]
					print(heaps(arr))



